Sparse Representation Of Data Research Articles

On the Fourier transform of a quantitative trait: Implications for compressive sensing

This paper explores the genotype-phenotype relationship. It outlines conditions under which the dependence of a quantitative trait on the genome might be predictable, based on measurement of a limited subset of genotypes. It uses the theory of real-valued Boolean functions in a systematic way to translate trait data into the Fourier domain. Important trait features, such as the roughness of the trait landscape or the modularity of a trait have a simple Fourier interpretation. Ruggedness at a gene location corresponds to high sensitivity to mutation, while a modular organization of gene activity reduces such sensitivity.Traits where rugged loci are rare will naturally compress gene data in the Fourier domain, leading to a sparse representation of trait data, concentrated in identifiable, low-level coefficients. This Fourier representation of a trait organizes epistasis in a form which is isometric to the trait data. As Fourier matrices are known to be maximally incoherent with the standard basis, this permits employing compressive sensing techniques to work from data sets that are relatively small—sometimes even of polynomial size—compared to the exponentially large sets of possible genomes.This theory provides a theoretical underpinning for systematic use of Boolean function machinery to dissect the dependency of a trait on the genome and environment.

Stratified Stochastic Variational Inference for High-Dimensional Network Factor Model

There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov chain Monte Carlo can be extremely slow and show poor mixing, thereby motivating research on alternative algorithms that scale well in high-dimensional settings. In this article, we focus on the latent factor model, a widely used approach for latent space modeling of network data. We develop scalable algorithms to conduct approximate Bayesian inference via stochastic optimization. Leveraging sparse representations of network data, the proposed algorithms show massive computational and storage benefits, and allow to conduct inference in settings with thousands of nodes. An R package with an efficient c++ implementation of the proposed algorithms is provided.

A Sparse Representation of Social Media, Internet Query, and Surveillance Data to Forecast Dengue Case Number using Hybrid DecompositionBidirectional LSTM

A Sparse Representation of Social Media, Internet Query, and Surveillance Data to Forecast Dengue Case Number using Hybrid DecompositionBidirectional LSTM

Subtype-WESLR: identifying cancer subtype with weighted ensemble sparse latent representation of multi-view data

The discovery of cancer subtypes has become much-researched topic in oncology. Dividing cancer patients into subtypes can provide personalized treatments for heterogeneous patients. High-throughput technologies provide multiple omics data for cancer subtyping. Integration of multi-view data is used to identify cancer subtypes in many computational methods, which obtain different subtypes for the same cancer, even using the same multi-omics data. To a certain extent, these subtypes from distinct methods are related, which may have certain guiding significance for cancer subtyping. It is a challenge to effectively utilize the valuable information of distinct subtypes to produce more accurate and reliable subtypes. A weighted ensemble sparse latent representation (subtype-WESLR) is proposed to detect cancer subtypes on heterogeneous omics data. Using a weighted ensemble strategy to fuse base clustering obtained by distinct methods as prior knowledge, subtype-WESLR projects each sample feature profile from each data type to a common latent subspace while maintaining the local structure of the original sample feature space and consistency with the weighted ensemble and optimizes the common subspace by an iterative method to identify cancer subtypes. We conduct experiments on various synthetic datasets and eight public multi-view datasets from The Cancer Genome Atlas. The results demonstrate that subtype-WESLR is better than competing methods by utilizing the integration of base clustering of exist methods for more precise subtypes.

A Method for Reducing Timing Jitter’s Impact in Through-Wall Human Detection by Ultra-Wideband Impulse Radar

Ultra-wideband (UWB) impulse radar is widely used for through-wall human respiration detection due to its high range resolution and high penetration capability. UWB impulse radar emits very narrow time pulses, which can directly obtain the impulse response of the target. However, the time interval between successive pulses emitted is not ideally fixed because of timing jitter. This results in the impulse response position of the same target not being fixed, but it is related to slow-time. The clutter scattered by the stationary target becomes non-stationary clutter, which affects the accurate extraction of the human respiration signal. In this paper, we propose a method for reducing timing jitter’s impact in through-wall human detection by UWB impulse radar. After the received signal is processed by the Fast Fourier transform (FFT) in slow-time, we model the range-frequency matrix in the frequency domain as a superposition of the low-rank representation of jitter-induced clutter data and the sparse representation of human respiratory data. By only extracting the sparse component, the impact of timing jitter in human respiration detection can be reduced. Both numerical simulated data and experimental data demonstrate that our proposed method can effectively remove non-stationary clutter induced by timing jitter and improve the accuracy of the human target signal extraction.

Robust high-dimensional seismic data interpolation based on elastic half norm regularization and tensor dictionary learning

Due to the limitations imposed by acquisition cost, obstacles, and inaccessible regions, the originally acquired seismic data are often sparsely or irregularly sampled in space, which seriously affects the ability of seismic data to image underground structures. Fortunately, compressed sensing provides theoretical support for interpolating and recovering irregularly or undersampled data. Under the framework of compressed sensing, we have adopted a robust interpolation method for high-dimensional seismic data, based on elastic half norm regularization and tensor dictionary learning. Inspired by the elastic net, we first develop the elastic half norm regularization as a sparsity constraint, and we establish a robust high-dimensional interpolation model with this technique. Then, considering the multidimensional structure and spatial correlation of seismic data, we introduce a tensor dictionary learning algorithm to train a high-dimensional adaptive tensor dictionary from the original data. This tensor dictionary is used as the sparse transform for seismic data interpolation because it can capture more detailed seismic features to achieve the optimal and fast sparse representation of high-dimensional seismic data. Finally, we solve the robust interpolation model by an efficient iterative thresholding algorithm in the transform space and perform the space conversion by a modified imputation algorithm to recover the wavefields at the unobserved spatial positions. We conduct high-dimensional interpolation experiments on model and field seismic data on a regular data grid. Experimental results demonstrate that this method has superior performance and higher computational efficiency in noise-free and noisy seismic data interpolation, compared to extensively used dictionary learning-based interpolation methods.

Hospital readmission prediction based on improved feature selection using grey relational analysis and LASSO

PurposeThis paper develops a robust hospital readmission prediction framework by combining the feature selection algorithm and machine learning (ML) classifiers. The improved feature selection is proposed by considering the uncertainty in patient's attributes that leads to the output variable.Design/methodology/approachFirst, data preprocessing is conducted which includes how raw data is managed. Second, the impactful features are selected through feature selection process. It started with calculating the relational grade of each patient towards readmission using grey relational analysis (GRA) and the grade is used as the target values for feature selection. Then, the influenced features are selected using the Least Absolute Shrinkage and Selection Operator (LASSO) method. This proposed method is termed as Grey-LASSO feature selection. The final task is the readmission prediction using ML classifiers.FindingsThe proposed method offered good performances with a minimum feature subset up to 54–65% discarded features. Multi-Layer Perceptron with Grey-LASSO gave the best performance.Research limitations/implicationsThe performance of Grey-LASSO is justified in two readmission datasets. Further research is required to examine the generalisability to other datasets.Originality/valueIn designing the feature selection algorithm, the selection on influenced input variables was based on the integration of GRA and LASSO. Specifically, GRA is a part of the grey system theory, which was employed to analyse the relation between systems under uncertain conditions. The LASSO approach was adopted due to its ability for sparse data representation.

Random noise attenuation in seismic data using Hankel sparse low-rank approximation

The Hankel matrix’s low-rank property derived from the noise-free seismic data describing a few linear events and has been successively leveraged in many low-rank seismic data de-noising approaches. In such rank reduction methods, the typical scheme is to determine the best low-rank estimation of the formulated Hankel matrix, and then obtain the de-noised data. However, if the noisy data has been rearranged for the low-rank approximation in a Hankel matrix, it is usually not precisely low-rank. In the presented research, we propose a multivariate generalization of the minimax-concave penalty (MCP) function inducing sparsity on seismic data in the time-space domain. Initially obtained sparse representation of data would be decomposed into semi low-rank and the sparse components with the best approximate of noisy measurement matrix would be defined. This would be performed through the low-rank matrix extraction by optimal (re)weighting of the singular vectors of the observed matrix. The efficiency of the proposed method was evaluated on synthetic and real land data examples. Results were also compared with the state-of-art methods such as the non-local means (NLM), the Optimum Shrinkage Sparse Low-Rank estimation, the Optimum Shrinkage Synchrosqueezing Wavelet Transform and the damped rank reduction (DRR) methods. Qualitative and quantitative comparison of results approved capabilities of the proposed method compared to other selected noise attenuation method.

An Improved Data Fusion Method for Water Quality Sensors

This paper proposes an improved data fusion method for water quality sensors. First, a deep learning network model is formed by stacking automatic encoder and sparse automatic encoder, so as to realize feature mining and sparse representation of sample data. Second, after large-scale sample training, the network model may fit complex nonlinear functions, and has certain generalization ability for low-quality sample data. As a result, the accuracy of prediction and classification can be improved. The experimental results demonstrate that the proposed method can obtain higher classification accuracy.

Linear-time cluster ensembles of large-scale single-cell RNA-seq and multimodal data.

A fundamental task in single-cell RNA-seq (scRNA-seq) analysis is the identification of transcriptionally distinct groups of cells. Numerous methods have been proposed for this problem, with a recent focus on methods for the cluster analysis of ultralarge scRNA-seq data sets produced by droplet-based sequencing technologies. Most existing methods rely on a sampling step to bridge the gap between algorithm scalability and volume of the data. Ignoring large parts of the data, however, often yields inaccurate groupings of cells and risks overlooking rare cell types. We propose method Specter that adopts and extends recent algorithmic advances in (fast) spectral clustering. In contrast to methods that cluster a (random) subsample of the data, we adopt the idea of landmarks that are used to create a sparse representation of the full data from which a spectral embedding can then be computed in linear time. We exploit Specter's speed in a cluster ensemble scheme that achieves a substantial improvement in accuracy over existing methods and identifies rare cell types with high sensitivity. Its linear-time complexity allows Specter to scale to millions of cells and leads to fast computation times in practice. Furthermore, on CITE-seq data that simultaneously measures gene and protein marker expression, we show that Specter is able to use multimodal omics measurements to resolve subtle transcriptomic differences between subpopulations of cells.

Effect of Sparse Representation of Time Series Data on Learning Rate of Time-Delay Neural Networks

In this paper, we examine how sparsifying input to a time-delay neural network (TDNN) can significantly improve the learning time and accuracy of the TDNN for time series data. The sparsifying of input is done through a sparse transform input layer. Many applications that involve prediction or forecasting of the state of a dynamic system can be formulated as a time series forecasting problem. Here, the task is to forecast some state variable, which is represented as a time series in applications such as weather forecasting, energy consumption prediction or predicting future state of a moving object. While there are many tools for time-delay forecasting, TDNNs have recently received more attention. We show that through applying a sparsifying input transform layer to the TDNN, we can considerably improve the learning time and accuracy. Through analyzing the learning process, we demonstrate the mathematical reasons for this improvement. Experiments with several datasets are used to show the improvement and the reason behind it. We use data from national weather forecast datasets, vehicle speed time series and synthetic data. Several different sparse representations are evaluated including principal component analysis (PCA), discrete cosine transform (DCT) and a mixture of DCT and Haar transforms. It is observed that the higher sparsity leads to better performance. The relative simplicity of TDNNs, compared with deep networks, and the use of sparse transforms for quicker learning open up possibilities for online learning in small embedded devices that do not have powerful computing capabilities.

Demixed Sparse Principal Component Analysis Through Hybrid Structural Regularizers

Recently, the sparse representation of multivariate data has gained great popularity in real-world applications like neural activity analysis. Many previous analyses for these data utilize sparse principal component analysis (SPCA) to obtain a sparse representation. However, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{0}$ </tex-math></inline-formula> -norm based SPCA suffers from non-differentiability and local optimum problems due to non-convex regularization. Additionally, extracting dependencies between task parameters and feature responses is essential for further analysis while SPCA usually generates components without demixing these dependencies. To address these problems, we propose a novel approach, demixed sparse principal component analysis (dSPCA), that relaxes the non-convex constraints into convex regularizers, e.g., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> -norm and nuclear norm, and demixes dependencies of feature response on various task parameters by optimizing the loss function with marginalized data. The sparse and demixed components greatly improve the interpretability of the multivariate data. We also develop a parallel proximal algorithm to accelerate the optimization for hybrid regularizers based on our method. We provide theoretical analyses for error bound and convergency. We apply our method on simulated datasets to evaluate its time cost, the ability to explain the demixed information, and the ability to recover sparsity for the reconstructed data. Finally, we successfully separate the neural activity into different task parameters like stimulus or decision, and visualize the demixed components based on the real-world dataset.

Efficient Sparse Coding Using Hierarchical Riemannian Pursuit

Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in various image and video processing tasks. However, classical methods learn the dictionary and the sparse code based on alternating optimizations, usually without theoretical guarantees for either optimality or convergence due to non-convexity of the problem. Recent works on sparse coding with a complete dictionary provide strong theoretical guarantees thanks to the development of the non-convex optimization. However, initial non-convex approaches learn the dictionary in the sparse coding problem sequentially in an atom-by-atom manner, which leads to a long execution time. More recent works seek to directly learn the entire dictionary at once, which substantially reduces the execution time. However, the associated recovery performance is degraded with a finite number of data samples. In this paper, we propose an efficient sparse coding scheme with a two-stage optimization. The proposed scheme leverages the global and local Riemannian geometry of the two-stage optimization problem and facilitates fast implementation for superb dictionary recovery performance by a finite number of samples without atom-by-atom calculation. We further prove that, with high probability, the proposed scheme can exactly recover any atom in the target dictionary with a finite number of samples if it is adopted to recover one atom of the dictionary. An application on wireless sensor data compression is also proposed. Experiments on both synthetic and real-world data verify the efficiency and effectiveness of the proposed scheme.

DeepCEDNet: An Efficient Deep Convolutional Encoder-Decoder Networks for ECG Signal Enhancement

Electrocardiogram (ECG) signal can be thought of as an effective indicator for detection of various arrhythmias. However, the acquired ECG data is always corrupted by amounts of noise, which have a great influence on the diagnosis of cardiovascular diseases. In this paper, an efficient deep convolutional encoder-decoder network framework is proposed to remove the noise from ECG signal, which is termed as ‘DeepCEDNet’. This network is able to learn a sparse representation of data in the time-frequency domain via the high-order synchrosqueezing transform (FSSTH) and a nonlinear function that maps the noisy data into the clean one based on the distribution difference between signal and noise from the training set. Extensive experiments are conducted on ECG signals from the MIT-BIH Arrhythmia database and MIT-BIH Long-Term ECG database, and the added noise is obtained from the MIT-BIH Noise Stress Test database. The denoising performance is evaluated by means of signal to noise ratio (SNR), root mean squared error (RMSE) and percent root mean square difference (PRD). The results indicate that the proposed DeepCEDNet can obtain superior performance in both noise reduction and details preservation with higher SNR and lower RMSE and PRD compared to the traditional convolutional neural network (CNN) and the fully convolutional network-based denoising auto-encoder (FCN). We believe that the DeepCEDNet has a wide application prospect in the biomedical field.

Sparse representation of complex-valued fMRI data based on spatiotemporal concatenation of real and imaginary parts

BackgroundSpatial sparsity has been found to be in line with the intrinsic characteristic of brain activation. However, identifying a sparse representation of complex-valued fMRI data is challenging due to high noise within the phase data. New methodsWe propose to reduce the noise by combining real and imaginary parts of complex-valued fMRI data along spatial and temporal dimensions to form a real-valued spatiotemporal concatenation model. This model not only enables flexible usage of existing real-valued sparse representation algorithms but also allows for the reconstruction of complex-valued spatial and temporal components from their real and imaginary estimates. We propose to select components from both real and imaginary estimates to reconstruct the complex-valued component, using phase denoising to recover weak brain activity from high-amplitude noise. ResultsThe K-SVD algorithm was used to obtain a sparse representation within the spatiotemporal concatenation model. The results from simulated and experimental complex-valued fMRI datasets validated the efficacy of our method. Comparison with existing methodsCompared to a magnitude-only approach, the proposed method detected additional voxels manifest within several specific regions expected to be involved but likely missing from the magnitude-only data, e.g., in the anterior cingulate cortex region. Simulation results showed that the additional voxels were accurate and unique information from the phase data. Compared to a complex-valued dictionary learning algorithm, our method exhibited lower noise for both magnitude and phase maps. ConclusionsThe proposed method is robust to noise and effective for identifying a sparse representation of the natively complex-valued fMRI data.

FOUR-DIMENSIONAL ENCODING OF CHARACTER SEQUENCES AND EVALUATION OF THEIR SIMILARITIES AND DIFFERENCES

This paper describes a string encoding algorithm, which produces sparse dis-tributed representations (SDR) of text data. In essence, this is a modified version of a prior algorithm and the modifications have the following benefits: - the ability to decode data, without loss of information; - greatly increased capacity of the encoding space; - the possibility of performing more detailed comparisons of encoded strings. The main disadvantage compared to the prior algorithm is the increased complexity of the procedure for encoded string comparison. This is due to the use of a four-dimensional encoding space, instead of a two-dimensional space.

Matching pursuit-based sparse spectral analysis: Estimating frequency-dependent anomalies from nonstationary seismic data

Spectral decomposition has been widely used to detect frequency-dependent anomalies associated with hydrocarbons. By ignoring the time-variant feature of the frequency content of individual reflected wavelets, we have adopted a sparse time-frequency spectrum and developed a matching pursuit-based sparse spectral analysis (MP-SSA) method to estimate the sparse time-frequency representation of the seismic data. Further, we evaluate a generalized nonstationary convolution model concerning propagation attenuation and frequency-dependent reflectivity, and we mathematically evaluate the sparse time-frequency spectrum of the nonstationary seismic data as being equal to the product of the Fourier spectrum of the source wavelet, frequency-dependent reflection coefficient, and the cumulative attenuation during seismic wave propagation. Therefore, the reflectivity spectrum, which is a combination of the frequency-dependent reflectivity and the propagation attenuation, can be determined by dividing the sparse time-frequency spectrum of the seismic data by the Fourier spectrum of the source wavelet. Application of the matching pursuit-based decomposition methods to synthetic nonstationary convolutional data illustrates that the adopted MP-SSA spectrum shows a higher time resolution than the matching pursuit-based Wigner-Ville distribution and the matching pursuit-based instantaneous spectral analysis spectra. Notably, the MP-SSA method can avoid spectral smearing, which may introduce distortions to the frequency-dependent anomaly estimation. Application of the amplitude versus frequency analysis based on MP-SSA to field data illustrates the potential of using the sparse reflectivity spectral intercept and gradient to detect the hydrocarbon reservoirs.

Optimally Sparse Representations of Cartoon-Like Cylindrical Data

Sparse representations of multidimensional data have received a significant attention in the literature due to their applications in problems of data restoration and feature extraction. In this paper, we consider an idealized class $${\mathcal {C}}^2(Z) \subset L^2({\mathbb {R}}^3)$$ of 3-dimensional data dominated by surface singularities that are orthogonal to the xy plane. To deal with this type of data, we introduce a new multiscale directional representation called cylindrical shearlets and prove that this new approach achieves superior approximation properties not only with respect to conventional multiscale representations but also with respect to 3-dimensional shearlets and curvelets. Specifically, the N-term approximation $$f_N^S$$ obtained by selecting the N largest coefficients of the cylindrical shearlet expansion of a function $$f \in {\mathcal {C}}(Z)$$ satisfies the asymptotic estimate $$ \Vert f - f_N^S\Vert _2^2 \le c \, N^{-2} \, (\ln N)^3, \quad \text {as } N \rightarrow \infty .$$ This is the optimal decay rate, up the logarithmic factor, outperforming 3d wavelet and 3d shearlet approximations which only yield approximation rates of order $$N^{-1/2}$$ and $$N^{-1}$$ (ignoring logarithmic factors), respectively, on the same type of data.

An Attention-Based Deep Learning Method for Schizophrenia Patients Classification Using DNA Methylation Data.

In this paper, the classification problem of schizophrenia patients from healthy controls is considered, whose goal is to explore the relationship between DNA characteristics and schizophrenia. However, the DNA methylation data has the properties of small samples in high dimension and non-Gaussian distribution which makes it hard to do classification with DNA methylation data. Hence a classification method based on deep learning is designed. We propose a feature selection method based on attention mechanism which embeds a weight gated layer in the network structure to get a task-related sparse representation of the DNA methylation data. The performance of proposed method outperforms existing feature selection methods. On a real-world data set, the classification with proposed method achieves a high accuracy.

A note on the efficient evaluation of a modified Hilbert transformation

Abstract In this note we consider an efficient data–sparse approximation of a modified Hilbert type transformation as it is used for the space–time finite element discretization of parabolic evolution equations in the anisotropic Sobolev space H 1,1/2(Q). The resulting bilinear form of the first order time derivative is symmetric and positive definite, and similar as the integration by parts formula for the Laplace hypersingular boundary integral operator in 2D. Hence we can apply hierarchical matrices for data–sparse representations and for acceleration of the computations. Numerical results show the efficiency in the approximation of the first order time derivative. An efficient realisation of the modified Hilbert transformation is a basic ingredient when considering general space–time finite element methods for parabolic evolution equations, and for the stable coupling of finite and boundary element methods in anisotropic Sobolev trace spaces.